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2 years ago

8

Find two solutions to each equation in the interval -90°<θ<270°

1 answer:

UkoKoshka [18]2 years ago

8 0

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A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean

Nana76 [90]

Answer: 0.0026

Step-by-step explanation:

Given: Mean : $\mu=8.4\text{ hours}$

Standard Deviation : $\sigma = 1.8\text{ hours}$

Sample size : $n=40$

Formula to calculate z-score :-

$z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For X=7.6 hours.

$z=\dfrac{7.6-8.4}{\dfrac{1.8}{\sqrt{40}}}=-2.81091347571\approx-2.8$

$P(X$

Hence, the probability that their mean rebuild time is less than 7.6 hours = 0.0026

8 0

2 years ago

Read 2 more answers

What is the volume, in cubic in, of a cylinder with a height of 12in and a base radius of 6in, to the nearest tenths place?

Shtirlitz [24]

Answer:

1356.5 cubic inches

Step-by-step explanation:

Given information:

Height of the cylinder = 12 in.

Radius of base of the cylinder = 6 in.

We need to find volume of the cylinder.

Volume of cylinder:

$V=\pi r^2h$

where, r is the radius of base and h is height of the cylinder.

Substitute the given values in the above formula.

$V=\pi (6)^2(12)$

$V=(3.14)(36)(12)$ $[\because \pi=3.14]$

$V=1356.48$

Approx to nearest tenth.

$V\approx 1356.5$

Therefore, the volume of cylinder is 1356.5 cubic inches.

8 0

2 years ago

Name the postulate or theorem you can use to prove ∆ABD ≅ ∆CBD.

lozanna [386]

Hey there!

Triangle CBD is congruent to triangle ABD. This means that BD is congruent to BD by reflexive property. You have two congruent angles, and one congruent side. This would be AAS theorem. The answer is D.

I hope this helps!

5 0

2 years ago

Read 2 more answers

Find the area of quadrilateral ABCD. Round the area to the nearest whole number, if necessary. A(-5, 4) 4 B(0, 3) 2. F(-2, 1) -2

valentina_108 [34]

Answer:26

Step-by-step explanation:

5 0

2 years ago

Evaluate the line integral by the two following methods. xy dx + x2y3 dy C is counterclockwise around the triangle with vertices

nadezda [96]

Answer:

a)

$\frac{2}{3}$

b)

$\frac{2}{3}$

Step-by-step explanation:

a) The first part requires that we use line integral to evaluate directly.

The line integral is

$\int_C xydx + {x}^{2} {y}^{3} dy$

where C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2)

The boundary of integration is shown in the attachment.

Our first line integral is

$L_1 = \int_ {(0,0)}^{(1,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is y=0, x varies from 0 to 1.

When we substitute y=0 every becomes zero.

$\therefore \: L_1 =0$

Our second line integral is

$L_2 = \int_ {(1,0)}^{(1,2)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is:

$x = 0 \implies \: dx = 0$

y varies from 1 to 2.

We substitute the boundary and the values to get:

$L_2 = \int_ {1}^{2}1 \cdot y(0) + {1}^{2} \cdot \: {y}^{3} dy$

$L_2 = \int_ {1}^2 {y}^{3} dy = \frac{8}{3}$

The 3rd line integral is:

$L_3 = \int_ {(1,2)}^{(0,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is

$y = 2x \implies \: dy = 2dx$

x varies from 0 to 1.

We substitute to get:

$L_3 = \int_ {1}^{0} x \cdot \: 2xdx + {x}^{2} {(2x)}^{3}(2 dx)$

$L_3 = \int_ {1}^{0} 8 {x}^{5} + 2 {x}^{2} dx = - 2$

The value of the line integral is

$L = L_1 + L_2 + L_3$

$L = 0 + \frac{8}{3} + - 2 = \frac{2}{3}$

b) The second part requires the use of Green's Theorem to evaluate:

$\int_C xydx + {x}^{2} {y}^{3} dy$

Since C is a closed curve with counterclockwise orientation, we can apply the Green's Theorem.

This is given by:

$\int_C \: Pdx +Q \: dy = \int \int_ R \: Q_y - P_x \: dA$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int \int_ R \: 3 {x}^{2} {y}^{2} - y \: dA$

We choose our region of integration parallel to the y-axis.

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \int_ 0^{2x} \: 3 {x}^{2} {y}^{2} - y \: dydx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: {x}^{2} {y}^{3} - \frac{1}{2} {y}^{2} |_ 0^{2x} dx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: 8{x}^{5} - 2 {x}^{2} dx = \frac{2}{3}$

8 0

2 years ago